(6 points, 1 each part)Suppose we have a function g with domain (-,) is continuous and differentiable everywhere and with g'(52)=0.For each scenario below, decide if we can conclude that g(x) has a local minimum at x=52 from the information. If yes, write yes and explain briefly. If we cannot conclude this, explain why not briefly. (Words or picture can be used to explain why.)(a)g'(x)<0 for x<52 and g'(x)>0 for x>52(b)g'(x)>0 for x<52 and g'(x)<0 for x>52(c)g''(x)<0 for x<52 and g''(x)>0 for x>52(d)g''(52)<0(e)g''(52)>0(f)g(52)=0,g(2)=1, and g(3)=1.Modified from Gottlieb, Rates of Change.(8 pts) After the consumption of alcoholic beverage, the concentration of alcohol in the bloodstream (Blood Alcohol Consumption, BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The functionC(t)=1.35te-2.802tmodels the average BAC in mgml of a group of subjects t hours after rapid consumption of an alcoholic drink.a) Consider the interval [0,). Where is C(t) increasing? Where is C(t) decreasing?b) Does C(t) have an absolute (global) maximum on [0,)? If so, give the value and time it occurs and explain clearly how you know it is the absolute (global) maximum. If not, explain why not.(Hint: it might help to make a rough sketch of C(t) and where C is increasing and decreasing.)